CN109839272B - Bearing fault diagnosis method based on fault impact extraction and self-correlation ensemble averaging - Google Patents

Abstract

The invention discloses a bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging, which separates a Large Amplitude Impact (LAIT) signal section from a vibration signal of a bearing rolling body, performs band-pass filtering and envelope demodulation on the separated LAIT signal section, aligns phases of the LAIT signal section through an autocorrelation function, then performs ensemble averaging on the aligned LAIT signal section, and performs linear trend item elimination and regularization processing to generate an enhanced characteristic signal LAIT-AEA for judging whether a fault exists in the bearing. The bearing fault diagnosis method does not need to use a tachometer and an optical encoder, is insensitive to rotating speed fluctuation and rolling body sliding, and has the characteristics of high fault sensitivity and small calculated amount.

Description

Bearing fault diagnosis method based on fault impact extraction and self-correlation ensemble averaging

Technical Field

The invention relates to the technical field of fault diagnosis of rolling bearings, in particular to a bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging.

Background

The fault diagnosis of the rotary machine can provide support for maintenance decision, help to prevent mechanical failure and avoid major loss caused by mechanical failure, the fault diagnosis of the rotary machine is already active for decades, various effective signal processing methods are provided, and fault-sensitive features can be extracted under the condition of low signal-to-noise ratio.

Time domain synchronous averaging (TSA) is a widely recognized method of signal preprocessing to achieve enhanced diagnostics by increasing the characteristic signal-to-noise ratio. TSA divides a long signal x (t) into successive signal segments, the signal length being the period of the target signature. A synchronized ensemble averaged signal is then generated by synchronous averaging of the signal segments:

wherein, N is the number of signal segments, T is the period of the target signal, the amplitude-frequency characteristic of TSA is represented as a comb filter, the filter is composed of a series of band pass filters and sidebands which are uniformly distributed, the center frequency of the band pass filters is the rotating frequency of the rotating shaft and the higher harmonic thereof, therefore, noise and frequency components of which the frequency is not an integral multiple of the rotating frequency can be filtered by the filter.

Since the failure frequency of the gearbox is Z times the rotation frequency of the rotating shaft, Z being the number of teeth of the gear, the failure frequency can be successfully applied to the enhanced diagnosis of the gearbox through the comb filter TSA. The use of TSA for fault diagnosis of bearings presents a series of challenges:

first, amplitude modulation of the bearing fault signal can cause loss of diagnostic information. The inner ring and the rolling body of the bearing are moving parts, and the positions of the inner ring and the rolling body are constantly changed relative to the bearing area during the operation of the bearing. The closer the damaged moving part is to the load-bearing center, the greater the load is applied, and the greater the impact caused by the damage. The damage moving part continuously enters and leaves the bearing area, and the amplitude of the damage impact is increased and decreased repeatedly along with the damage moving part to form amplitude modulation. The signal section corresponding to the damaged part passing through the carrying region is a Large Amplitude Impact (LAIT) signal section. And the signal section corresponding to the damaged part when the damaged part leaves the bearing area is a Non-LAIT (Non-LAIT) signal section. The signal segments of a conventional TSA separation include both LAIT and Non-LAIT signal segments. If ensemble averaging is performed on the LAIT signal segments only, the resulting result (as shown in fig. 1 (a)) is significantly better than the result obtained by performing ensemble averaging on all signal segments (as shown in fig. 1 (b)), resulting in a larger synchronous averaged signal impact amplitude.

Second, phase errors between separate signal segments can also cause loss of diagnostic information. Because the ratio of the axial load to the radial load changes, when the rolling body rotates to different positions, the equivalent contact angle also changes. Thus, different rolling bodies have different equivalent rotation diameters and attempt to rotate at different speeds. But the cage limits the rolling bodies from their average position. Such a movement pattern causes the rolling elements to slide. Both rolling element slip and rotational speed fluctuations are unavoidable and they both cause phase errors between the split signals, i.e. the split signals are not exactly synchronized. Typically, the damage-induced shock is a damped oscillation that gradually decays, with the oscillation lasting for several natural frequency cycles, as shown in fig. 1 (a). Superimposing such oscillation waveforms, even a phase error of only 1/4 natural frequency cycles causes a large loss of information, as shown in fig. 1 (c). Moreover, since the natural frequency of bearings is often as high as thousands or even thousands of Hz, even as low as 2.5X 10^-4s phase error, the resulting loss of information is also not negligible.

Third, the bearing speed signal cannot be used as a trigger for performing TSA. As described above, strict synchronization between separate signals is critical to performing TSA. In order to ensure the synchronization of the separation signals, a tachometer or an encoder is usually used to measure the phase detection signal, and then angular domain resampling is performed on the vibration signal according to the phase detection signal. Namely, each time the shaft rotates for one circle, an integral number of sampling points are collected at equal angles. Then, synchronous averaging is carried out by taking the frequency conversion as a trigger, and harmonic components of the frequency conversion can pass through the comb filter. Since the frequency of failure of the bearing is not an integer multiple of the rotational frequency, the rotational speed signal cannot be used as a phase detection signal to perform TSA.

Nevertheless, researchers have attempted to use TSA for enhanced fault diagnosis of rolling bearings. Siegel et al propose an envelope synchronous averaging method without an encoder using the outer ring fault frequency as a trigger signal for detecting different degrees of bearing outer ring damage. McFadden (microphone)Farden) and tozyy (zhaiyi) design a TSA scheme for fault diagnosis of the bearing inner ring. Because of inner ring failure frequency f_BPICage frequency f_cAnd frequency conversion f_rSatisfies the relationship f_BPI＝(f_r-f_c) Thus, the relative frequency (f) can be used_r-f_c) As a trigger signal, TSA is performed. However, this averaging method can only be used to detect inner ring faults and requires measuring the cage frequency, which is not feasible in engineering using embedded sensors inside the bearing. In addition, the LAIT signal section and the Non-LAIT signal section are used together with conventional diagnostic methods such as a dither method (HFRT), Empirical Mode Decomposition (EMD), spectral Kurtogram method, Square Envelope Spectrum (SES), and Modulated Signal Bispectrum (MSB).

In view of this, it is an urgent technical problem to be solved by those skilled in the art to develop a method for extracting and separating large-amplitude impact signal segments to perform ensemble averaging to determine a bearing fault.

Disclosure of Invention

The invention aims to provide a bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging, which comprises the steps of extracting and separating LAIT signal sections, generating an enhanced fault characteristic signal for each rolling element through processing such as band-pass filtering, envelope demodulation, autocorrelation ensemble averaging, trend removing items, regularization and the like, and further judging whether a fault exists in a bearing.

In order to solve the technical problem, the invention provides a bearing fault diagnosis method based on fault impact extraction and self-correlation ensemble averaging, which comprises the following steps:

s1, setting an initial phase of a rolling body of the bearing, and extracting and separating a corresponding LAIT signal section when the rolling body passes through a bearing center;

s2, performing band-pass filtering and envelope demodulation on each LAIT signal segment separated in the step S1;

s3, aligning the LAIT signal segment in the step S2 through autocorrelation;

and S4, carrying out ensemble averaging on the LAIT signal sections after phase alignment in the step S3, carrying out linear trend item elimination and regularization processing on ensemble averaged signals to generate enhanced characteristic signals LAIT-AEA, and judging whether the bearing has rolling element faults or not according to the enhanced characteristic signals LAIT-AEA.

Preferably, the length of the LAIT signal segment extracted and separated in step S1 is three rotation periods of the rolling element.

Preferably, the specific steps of extracting and separating the LAIT signal segment corresponding to the rolling element passing through the bearing center in step S1 are as follows:

s101, setting the frequency f of the retainer for the rolling bodies to revolve around the center of the rotating shaft along with the retainer_cThe frequency of the rolling bodies rotating around the centers of the rolling bodies is f_BSThe angle theta of the rolling body rotating around the center of the rotating shaft in one rotation period can be obtained_sComprises the following steps:

θ_s＝2πf_c·T_BS (1)

in the formula (1), T_BS＝1/f_BSThe self-rotation period of the rolling body is T, the corresponding fault period of the rolling body is T_B＝T_BSA fault frequency of f_B＝1/T_B；

S102, setting a rotation period T_BSThe first rolling element passing through the bearing center is designated by the number one rolling element, denoted by RE₁The rolling elements which subsequently pass through the bearing centre are respectively defined as RE₂,RE₃,…,RE_ZWherein Z is the number of rolling elements, then rolling element RE₁Initial phase of

Must satisfy the condition

It can be seen that the rolling elements RE_iCumulative phase corresponding to jth rotation period

Comprises the following steps:

in the formula (2), the reaction mixture is,

for said rolling body RE₁The phase of the jth autorotation period, delta-2 pi/Z is the central angle between two continuous rolling bodies;

s103, based on rolling element RE_iIt can be seen that the phase of the LAIT signal segment must satisfy the condition:

in the formula (3), the reaction mixture is,

to represent

The remainder of division by 2 π gives the rolling element RE from the formulae (2) and (3)_iThe LAIT signal segment of (1);

s104, according to the accumulated phase sequence in the step S102

Obtaining and accumulating the phase sequence

Corresponding time series t_i,jComprises the following steps:

the time condition of the LAIT separation is:

T_R-T_BS＜mod(t_i,j+T_BS,T_R)≤T_R(5)

in the formula (5), T_R＝1/f_cFor the rotation period of the retainer, the starting point of the LAIT signal segment is found out by the formula (4) and the formula (5), that is, the length is 3T_BSThe LAIT signal section is separated;

s105, setting the rolling bearing RE_iIs [ nu ] of the vibration signal₁,ν₂,…,ν_N]Length N, sampling frequency f_sThen the rolling body RE_iMay form a sequence T_iComprises the following steps:

in the formula (6), the reaction mixture is,

is a real number, t_i,1＝t₁-(i-1)δ/(2πf_c)，

Is RE_iIs detected by the phase angle of the phase-locked loop,

the number of the rotation periods is the same as the number of the rotation periods,

represents to Nf_BS/f_SRounding down, then the time sequence satisfying the formula (5) can be found out by the formula (6), and the index corresponding to the time sequence is the index D of the LAIT signal segment_iIt can be expressed as:

in the formula (7), the reaction mixture is,

is a natural number, d_i,kIs RE_iThe k-th LAIT signal segment of (a),

the number of LAIT signal segments, the separated rolling elements RE_iThe kth LAIT signal segment index of (a), can be expressed as:

M_i,k＝[ν(d_i,k),ν(d_i,k+1),ν(d_i,k+2),…,ν(d_i,k+(L₂-1))] (8)

in the formula (8), L₂＝[3T_BSf_s]The rounded length of the LAIT signal segment.

Preferably, each LAIT signal segment separated in step S2 is subjected to band-pass filtering to obtain a filtered LAIT signal segment, which is recorded as M'_i,kThen using Hilbert transform to M'_i,kEnvelope demodulation to obtain envelope signal E_i.k。

Preferably, the band-pass filter is a resonance frequency band centered on the natural frequency and having several fault frequency sidebands on both sides or a frequency band having a large amplitude energy concentration.

Preferably, the specific implementation method of step S3 is as follows:

s301, representing the damage impact component of the LAIT signal segment as

Wherein

For the initial phase of the impact, t is time, the autocorrelation function of the damage impact can be expressed as:

in the formula (9), tau is time delay, A represents fault impact amplitude of LAIT signal segment, and omega represents fault period T_BCorresponding to the angular velocity, equation (9) can be expressed as:

in the formula (10), θ represents a phase,

s302, according to the autocorrelation function in the step S301, the envelope signal E of the LAIT signal segment is processed_i.kThe autocorrelation function of (a) is expressed as:

R_i,k(τ)＝[r_i,k(τ₁),r_i,k(τ₂),r_i,k(τ₃),…,r_i,k(τ_L2)] (11)

in the formula (11), r_i,kIs a component of the autocorrelation function.

Preferably, the specific implementation method of step S4 is:

s401, carrying out overall average on the LAIT signal section of the autocorrelation alignment phase in the step S3 to obtain the rolling body RE_iIs the ensemble average a of the autocorrelation function_iI.e. said rolling elements RE_iIs expressed as:

in the formula (12), τ_jK is the number of LAIT signal segments for the time delay of the LAIT signal segments.

S402, for each rolling element RE in the step S401_iThe overall average characteristic signal is subjected to linear trend item elimination and regularization processing to obtain an enhanced characteristic signal LAIT-AEA；

And S403, judging whether the bearing has rolling element faults or not through the enhanced characteristic signal LAIT-AEA.

Preferably, said rolling elements RE_iThe linear trend term rejection formula of the overall average characteristic signal is as follows:

in the formula (13), the reaction mixture is,

is to A_iLeast squares linear fit of (a).

Preferably, said rolling elements RE_iThe regularization processing formula of the ensemble averaged feature signal is as follows:

compared with the prior art, the invention has the following beneficial technical effects:

(1) according to the invention, the problem of fault information loss caused by amplitude modulation of the bearing fault signal is solved by extracting and separating the LAIT signal section;

(2) in the invention, the phase of the LAIT signal segment is aligned by adopting the autocorrelation function, so that the problem of fault information loss caused by phase error is solved, the method is insensitive to rotation speed fluctuation and rolling body sliding, and the fault sensitivity of the method is effectively improved;

(3) according to the invention, the separated LAIT signal section is subjected to noise reduction treatment through band-pass filtering and envelope demodulation, so that the effectiveness of the LAIT signal section is greatly improved, and the fault sensitivity of the method is further enhanced;

(4) in the invention, a tachometer or an optical encoder is not needed, all signal processing flows are applied to the separated LAIT signal segment, and the method has the characteristic of small calculation amount.

Drawings

Figure 1 is a prior art schematic diagram of averaging signal segments for different transient conditions,

FIG. 2 is a flow chart of the bearing fault diagnosis method based on fault impact and autocorrelation ensemble averaging according to the present invention,

figure 3 is a schematic diagram of the motion of the rolling bodies of the bearing in the invention,

FIG. 4 is a schematic structural diagram of a mechanical failure simulation test platform in the invention,

FIG. 5 is a signal diagram of test data of a mechanical fault simulation test platform and a signal diagram of the test data analyzed and processed by Kurtogram,

FIG. 6 is a signal diagram of the mechanical fault simulation test platform test data signal analyzed and processed by the bearing fault diagnosis method of the present invention,

figure 7 is a signal diagram of the analysis processing of the test data signal for a normal bearing by Kurtogram,

fig. 8 is a signal diagram for analyzing and processing a test data signal of a normal bearing by the bearing fault diagnosis method of the present invention,

figure 9 is a signal diagram of a bearing fault data signal published by the bearing data center of university of west depot by Kurtogram,

fig. 10 is a signal diagram for analyzing and processing a bearing fault data signal published by the bearing data center of west university of storage by the bearing fault diagnosis method of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the present invention is further described in detail below with reference to the accompanying drawings.

As shown in fig. 2, a bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging, the method comprises the following steps:

s1, setting an initial phase of a rolling body of the bearing, and extracting and separating a corresponding LAIT signal section when the rolling body passes through a bearing center;

s2, performing band-pass filtering and envelope demodulation on each LAIT signal segment separated in the step S1;

s3, aligning the LAIT signal segment in the step S2 through autocorrelation;

and S4, carrying out ensemble averaging on the LAIT signal sections after phase alignment in the step S3, carrying out linear trend item elimination and regularization processing on ensemble averaged signals to generate enhanced characteristic signals LAIT-AEA, and judging whether the bearing has rolling element faults or not according to the enhanced characteristic signals LAIT-AEA.

In this embodiment, a LAIT signal segment is extracted and separated from a vibration signal of the bearing rolling element, then the separated LAIT signal segment is subjected to noise reduction processing, finally the phases of the LAIT signal segments are aligned through an autocorrelation function, the aligned LAIT signal segments are subjected to ensemble averaging, an enhanced characteristic signal LAIT-AEA is generated, and whether the bearing has a fault is judged through the enhanced characteristic signal LAIT-AEA.

In order to better understand the bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging, the steps of the method are described in detail below.

As shown in fig. 2, the LAIT signal length extracted and separated in step S1 is three rotation cycles of the rolling elements. In this embodiment, the length of the LAIT signal segment extracted and separated in this embodiment is equal to three rotation periods of the rolling element, in order to better extract the impact information, considering that the longer the separated LAIT signal segment is, the more the impact attenuation pulses are included.

As shown in fig. 2 and 3, the specific steps of extracting and separating the LAIT signal segment corresponding to the rolling element passing through the bearing center in step S1 are as follows:

s101, setting the frequency f of the retainer for the rolling bodies to revolve around the center of the rotating shaft along with the retainer_cThe frequency of the rolling bodies rotating around the centers of the rolling bodies is f_BSThe angle theta of the rolling body rotating around the center of the rotating shaft in one rotation period can be obtained_sComprises the following steps:

θ_s＝2πf_c·T_BS (1)

in the formula (1), T_BS＝1/f_BSThe self-rotation period of the rolling body is T, the corresponding fault period of the rolling body is T_B＝T_BSA fault frequency of f_B＝1/T_B；

S102, setting a rotation period T_BSThe first rolling element passing through the bearing center is designated by the number one rolling element, denoted by RE₁The rolling elements which subsequently pass through the bearing centre are respectively defined as RE₂,RE₃,…,RE_ZWherein Z is the number of rolling elements, then rolling element RE₁Initial phase of

Must satisfy the condition

It can be seen that the rolling elements RE_iCumulative phase corresponding to jth rotation period

Comprises the following steps:

in the formula (2), the reaction mixture is,

for said rolling body RE₁The phase of the jth rotation cycle, δ 2 π/Z, is the central angle between two consecutive rolling elements, and rolling element RE can be obtained from equation (2)_iAll accumulated phases of

S103, based on rolling element RE_iIt can be seen that the phase of the LAIT signal segment must satisfy the condition:

in the formula (3), the reaction mixture is,

to represent

The remainder of division by 2 π gives the rolling element RE from the formulae (2) and (3)_iThe LAIT signal segment of (1);

s104, according to the accumulated phase sequence in the step S102

Obtaining and accumulating the phase sequence

Corresponding time series t_i,jComprises the following steps:

the time condition for the LAIT signal segment separation is:

T_R-T_BS＜mod(t_i,j+T_BS,T_R)≤T_R (5)

in the formula (5), T_R＝1/f_cFor the rotation period of the retainer, the starting point of the LAIT signal segment is found out by the formula (4) and the formula (5), that is, the length is 3T_BSThe LAIT signal section is separated;

s105, setting the rolling bearing RE_iIs [ nu ] of the vibration signal₁,ν₂,…,ν_N]Length N, sampling frequency f_sThen the rolling body RE_iEach rotation ofThe time phase of the cycle may form a sequence T_iComprises the following steps:

in the formula (6), the reaction mixture is,

is a real number, t_i,1＝t₁-(i-1)δ/(2πf_c)，

Is RE₁Is detected by the phase angle of the phase-locked loop,

the number of the rotation periods is the same as the number of the rotation periods,

represents to Nf_BS/f_SRounding down, then the time sequence satisfying the formula (5) can be found out by the formula (6), and the index corresponding to the time sequence is the index D of the LAIT signal segment_iIt can be expressed as:

in the formula (7), the reaction mixture is,

is a natural number, d_i,kIs RE_iThe k-th LAIT signal segment of (a),

the number of LAIT signal segments, the separated rolling elements RE_iThe kth LAIT signal segment index of (a), can be expressed as:

M_i,k＝[ν(d_i,k),ν(d_i,k+1),ν(d_i,k+2),….ν(d_i,k+(L₂-1))] (8)

in the formula (8), L₂＝[3T_BSf_s]The rounded length of the LAIT signal segment.

In this embodiment, f in the step S101_cAnd f_BSIs shown as

And

wherein f is_rFor the rotation frequency of the rotating shaft, D is the pitch diameter of the bearing, D is the diameter of the rolling body, alpha is the contact angle, and for each rolling body RE_iAll can calculate the phase sequence T of the rotation period_iThen through its phase sequence T_iFind out the index D corresponding to LAIT signal segment_iThe rolling element RE can be constructed_iLAIT signal segment matrix M_i：

Wherein M is_i,kAs rolling bodies RE_iThe kth LAIT signal segment of (1).

In this embodiment, RE in FIG. 3₁For example, Spin 2 is RE₁The first LAIT signal segment is in autorotation period, Spin8 is RE₁The second LAIT signal segment is in autorotation period, and so on. Spin 2, and a previous Spin period (Spin 1) and a next Spin period (Spin 3) thereof, wherein signal sections corresponding to the three Spin periods are RE₁The first LAIT signal segment of (a); similarly, Spin8, and the previous Spin period (Spin 7) and the next Spin period (Spin 9) thereof, where the signal segments corresponding to the three Spin periods are RE₁The second LAIT signal segment of (a); and so on.

As shown in fig. 2, band-pass filtering is performed on each LAIT signal segment separated in step S2 to obtain filtered LAIT signal segments, which are denoted as M'_i,kThen using HilbertSpecial transform pair M_i,kEnvelope demodulation to obtain envelope signal E_i.k。

In this embodiment, first, noise reduction is performed on the LAIT signal segment through band-pass filtering, and in order to extract low-frequency impulse components from the high-frequency carrier, hilbert transform is used to demodulate the filtered LAIT signal segment, so as to obtain an envelope signal E_i.kEnvelope signal matrix E thereof_iCan be expressed as:

wherein, E'_i,k＝|M′_i,k+iH(M′_i,k) Is M'_i,kAnalysis Signal of (H'_i,k) Is M'_i,kThe hilbert transform.

As shown in fig. 2, the band-pass filter is a resonance band centered on the natural frequency and having several side bands of the fault frequency on both sides or a band having a large amplitude energy concentration. In this embodiment, in order to reduce the influence of the resonance frequency band on the bearing fault diagnosis result, the band-pass filtering selects and uses one of methods such as a fast Kurtogram (fast Kurtogram), a wavelet Kurtogram (wavelet Kurtogram), or an autocorrelation spectrum Kurtogram (Autogram) to search for the optimal resonance frequency band, and performs noise reduction on the LAIT signal segment.

As shown in fig. 2, the specific implementation method of step S3 is as follows:

s301, representing the damage impact component in the LAIT signal segment as

Wherein

For the initial phase of the impact, t is time, the autocorrelation function of the damage impact can be expressed as:

in the formula (9), tau is time delay, A represents the amplitude of the damage impact component in the LAIT signal segment, and omega represents the fault period T_BCorresponding angular velocity, wherein T_B＝2π/ω，ω＝2πf_BThen equation (9) can be expressed as:

in the formula (10), θ represents a phase,

s302, obtaining the LAIT signal segment envelope signal E according to the autocorrelation function in the step S301_i.kIs expressed as:

R_i,k(τ)＝[r_i,k(τ₁),r_i,k(τ₂),r_i,k(τ₃),…,r_i,k(τ_L2)] (11)

in the formula (11), r_i,kIs a component of the autocorrelation function.

As shown in fig. 2, the specific implementation method of step S4 is as follows:

s401, the LAIT signal segment of the phase aligned through autocorrelation in the step S3 is subjected to overall average to obtain the rolling element RE_iAutocorrelation ensemble averaging of A_iI.e. said rolling elements RE_iIs expressed as:

in the formula (12), τ_jThe time delay of the LAIT signal segment is shown, and K is the number of the LAIT signal segments;

s402, for each rolling element RE in the step S401_iAnd performing linear trend item elimination and regularization processing on the overall average characteristic signal to obtain an enhanced characteristic signal LAIT-AEA.

And S403, judging whether the bearing has rolling element faults or not through the enhanced characteristic signal LAIT-AEA.

In this embodiment, because a phase error exists between the split LAIT signal segments due to rotation speed fluctuation and rolling element sliding, the phases of the LAIT signal segments after noise reduction are aligned by autocorrelation, and then the LAIT signal segments after phase alignment are subjected to ensemble averaging to obtain the rolling element RE_iAnd can generate said rolling elements RE_iIs given by the autocorrelation function matrix R_i：

Wherein R is_i,jIs the LAIT envelope signal E_i,kAnd since the extracted LAIT signal segment is of finite length, there may be a trend term in the LAIT signal segment autocorrelation function, and in order to obtain a more comparable result, for each of the rolling elements RE obtained_iAnd (3) eliminating and regularizing the linear trend items of the overall average characteristic signals to obtain enhanced characteristic signals LAIT-AEA, and finally judging whether the bearing has rolling body faults or not according to the enhanced characteristic signals LAIT-AEA.

In this embodiment, the vibration signal of the faulty bearing is represented as:

ν(t)＝x(t)+h(t)+n(t)

where x (t) represents the damage impact component, h (t) represents other frequency components, and n (t) represents the background white noise, and since x (t), h (t), and n (t) are independent of each other, the autocorrelation function of v (t) can be expressed as:

R_vv(τ)＝R_xx(τ)+R_xh(τ)+R_hx(τ)+R_hh(τ)+R_hn(τ)+R_nn(τ)+R_nx(τ)+R_nh(τ)＝R_xx(τ)+R_hh(τ)+R_nn(τ)

white noise autocorrelation has a large amplitude only when τ is 0 and is negligible at other time delays, i.e., when R is 0_nn(tau > 0) approximately equal to 0, and other frequency components h (t) can be removed by methods such as band-pass filtering and envelope demodulation, so that when tau is greater than 0, the autocorrelation function of the vibration signal v (t) is mainly the damage impact component x (t), and when in actual operation, because the extraction length of the LAIT signal segment is limited, R of white noise is_nnValues will also be taken for τ > 0, but decrease progressively as the delay τ increases.

As shown in fig. 2, the rolling elements RE_iThe linear trend term rejection formula of the overall average characteristic signal is as follows:

in the formula (13), the reaction mixture is,

is to A_iLeast squares linear fit of (a).

As shown in FIG. 1, the rolling elements RE_iThe regularization processing formula of the ensemble averaged feature signal is as follows:

in this embodiment, the autocorrelation function is at time delay τ_jFor a period of failure T_BAnd rolling element rotation period T_BSThe values of (A) are respectively corresponding to fault characteristic frequency component and rotation frequency component, in order to highlight the rolling element RE_iIs in the fault period T_BAnd rolling element rotation period T_BSValue of (d), will be delayed by τ_jIs set to [0.5T ]_B,2.5T_B]I.e. only 0.5T is analyzed_B≤τ_j≤2.5T_BBy taking into account the values obtained for each of said rolling elements RE_iThe overall average characteristic signals are subjected to linear trend item elimination and regularization treatment, so that each rolling body RE is ensured_iThe minimum value of the enhanced feature signal LAIT-AEA of (a) is zero.

In order to prove the effectiveness of the bearing fault diagnosis method based on fault impact extraction and self-correlation ensemble averaging, which is provided by the invention, verification is performed through a mechanical fault simulation test platform.

As shown in FIG. 4, the mechanical failure simulation test platform for test verification comprises a driving motor 1, a bearing 2, an inertia wheel 3, a belt transmission structure 4, a bevel gear box 5, a crank link structure 6 and a reciprocating mechanism 7 with a spring, wherein the bearing 2 with local rolling body damage is installed on a left bearing seat, the inertia wheel 3 with the weight of 5kg is installed on a shaft, a vertical downward radial load is provided by means of the gravity of the inertia wheel 3 to stimulate the bearing failure response, the spring on the reciprocating mechanism 7 is used for providing a variable load, the variable load is transmitted to the motor to cause the rotation speed fluctuation, the ratio of the axial load and the radial load of the bearing is continuously changed by the other variable load, the equivalent pitch diameter and the contact angle of the bearing 2 are changed, and further the rolling body is caused to slide, and two acceleration sensors 8 are installed on the bearing seats. In order to verify the validity of the algorithm under the rotation speed fluctuations, a tachometer was used in the test for observing the fluctuations in the rotation speed.

The tested bearing model is MB ER-10K, the number Z of the rolling elements of the bearing is 8, the diameter D of the rolling elements is 7.9375mm, the pitch diameter D of the bearing is 33.5026mm, the designed contact angle alpha is 0, and the self-transmission frequency f of the rolling elements is_BS＝1.992f_rRevolution frequency f of rolling element_c＝0.3815f_rSampling frequency f_s25.6kHz, for testing vibration acceleration signals in the vertical and horizontal directions, respectively.

As shown in fig. 5, fig. 5(a) shows the vibration signal in the horizontal direction obtained by the test, the test duration L is 14s, fig. 5(b) shows the rotation speed value calculated from the rotation speed signal by the zero-crossing detection method, and it can be seen from the graph that the rotation speed fluctuates in the range of 18.9 Hz to 19.2Hz, and the average value is f_r19.06Hz, a failure frequency of 2f can be calculated_BS75.93Hz, and a fault period T_B＝1/(2f_BS) 0.0132s, and the cage frequency, i.e. the revolution frequency of the rolling elements, is f_c7.27Hz, so that each rolling element revolves during the test period

In a complete revolution, 101 LAIT signal segments can be separated for each rolling element.

Analysis of the vibration signal by Kurtogram revealed that the "optimum" Band selected by Kurtogram was 11,733-12,800 Hz, denoted by Band 1, as Band 1 is close to f, as shown in FIG. 5(c)_s2, and therefore, frequency spectrum aliasing occurs (as shown in fig. 5 (e)), it can be seen from the figure that, due to the existence of frequency spectrum aliasing, rotation speed fluctuation and rolling element sliding, a serious "spectrum smearing" phenomenon occurs to fault characteristic frequency and harmonic components thereof, the smeared frequency spectrum and strong background noise cause serious uncertainty to a diagnosis conclusion, and considering that there are not a few energy concentration frequency bands with large amplitude in an amplitude spectrogram (as shown in fig. 5(d)), the frequency bands are selected as candidate frequency bands, including Band 2: 1500-3600 Hz, Band 3: 4100-4500 Hz, Band 4: 4800-5620 Hz and Band 5: 9000-11,200 Hz, and the self-propagating frequency f in the Band 3 envelope spectrum can be seen from FIG. 5(f) by analyzing with the candidate frequency Band (taking Band 3 as an example)_BSAnd a failure frequency 2f_BSAlthough the characteristic frequency components of the signal in Band 3 are clearer than those in Band 1, smearing still exists and can be interfered by other nearby frequency components.

As shown in fig. 6, the LAIT signal segments in Band 1 and Band 3 are separated and AEA by the bearing fault diagnosis method of the present invention, and an enhanced characteristic signal LAIT-AEA is obtained (as shown in fig. 6(a) and fig. 6(b)), and it can be seen from the figure that the LAIT-AEA of all rolling elements has a time delay τ T_BAnd τ 2T_BClear impact exists in the position, which shows that the separated LAIT signal section has autorotation frequency and fault characteristic frequency components, and the bearing can be judged to have rolling body faults based on the autorotation frequency and the fault characteristic frequency components.

In order to demonstrate that the enhanced characteristic signal LAIT-AEA is only detected when the rolling element of the bearing fails at a time delay τ ═ T_BAnd τ 2T_BIn the presence of an impact, a set of normal signals is used below to verify the effectiveness of the bearing fault diagnosis method proposed by the present invention.

As shown in fig. 7, the rotation speed is at the average value f_rAbout 18.87Hz, corresponding to a fault frequency of 2f_BS75.18Hz, and a fault period of T_B0.0133s, and a cage frequency f_cWhen being 7.2Hz, the rolling body revolves with the retainer

Thus, 100 LAIT signal segments can be isolated for each rolling element. From fig. 7(c), it can be seen that the preferred resonance frequency Band of the Kurtogram analysis vibration signal is 8200-8400 Hz, which is expressed by Band 6, and the candidate frequency Band includes: band 7: 1400-2300 Hz, Band 8: 3400-4200 Hz, and Band 9: 9600-10,800 Hz (as shown in FIG. 7 (d)).

As shown in fig. 8, the LAIT signal segments in Band 6 and Band 7 are separated and AEA by the bearing fault diagnosis method of the present invention to obtain enhanced characteristic signal LAIT-AEA (as shown in fig. 8(a) and 8(b)), and it can be seen from the figure that LAIT-AEA obtained from all LAIT signal segments extracted from normal bearing vibration signals have a time delay τ T_BAnd τ 2T_BThere is no impact, which further demonstrates the effectiveness of the bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging of the present invention.

In order to further verify the effectiveness of the invention, a set of bearing fault data published by a bearing data center at Western University of Reserve (CWRU) is adopted to verify the bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging.

The test data in the embodiment is collected from the radial vibration of the bearing at the driving end of the test bed, the model of the bearing is 6205-2RS JEM SKF, the number Z of the rolling elements of the bearing is 8, the diameter D of the rolling elements is 7.9400mm, the pitch diameter D of the bearing is 39.0398mm, the designed contact angle alpha is 0, and the self-transmission frequency f of the rolling elements is f_BS＝2.3567f_rRevolution frequency f of rolling element_c＝0.39828f_rSampling frequency f_s＝12kHz。

As shown in FIG. 9, the bearing of this test had a rolling element implanted with a lesion having a width of 0.53mm, and FIG. 9(a) shows a vibration signal of data "222 DE", the rotational frequency of the rotating shaftf_r29.93Hz, corresponding to a fault frequency of 2f_BS171.09Hz, and a fault period T_B0.0071s, revolution frequency f of rolling body_cThe time length of the data is selected to be L-10 s at 11.92Hz, and the rolling body revolves along with the retainer in the time period

A complete revolution, therefore, 119 LAIT signal segments can be isolated for each rolling element.

It can be seen from fig. 9(b) that the optimal frequency Band of the Kurtogram analysis vibration signal is 3797 to 3844Hz, which is represented by Band 10, but the width of Band 10 is only 47Hz, which is much smaller than the fault frequency 141.09Hz, so the number of sidebands that can be accommodated in the frequency Band is 0, so Band 10 is not an effective resonance frequency Band, and considering that the amplitude is large in the frequency Band of 3000 to 3500Hz, there is energy concentration caused by suspected resonance, so the frequency Band of 3000 to 3500Hz is selected as the candidate frequency Band, which is represented by Band 11, and it can be seen from fig. 9(d) that the fault characteristic frequency and its harmonic component exist in the envelope spectrum in the frequency Band of Band 11, but the fault characteristic frequency and its harmonic component are seriously annihilated by background noise and rotation frequency, which is difficult to identify.

As shown in fig. 10, it can be seen from the figure that the fault characteristic signal LAIT-AEA calculated from the Band 2 in-Band signal by the bearing fault diagnosis method of the present invention has a time delay τ T_BAnd τ 2T_BAnd clear impact exists, and the existence of the rolling element fault of the bearing can be judged based on the existence of the two impacts.

The bearing fault diagnosis method based on fault impact extraction and self-correlation ensemble averaging provided by the invention is described in detail above. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the core concepts of the present invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.

Claims (4)

1. A bearing fault diagnosis method based on fault impact extraction and autocorrelation ensemble averaging is characterized by comprising the following steps:

s1, setting an initial phase of a rolling body of the bearing, and extracting and separating a corresponding LAIT signal section when the rolling body passes through a bearing center;

s2, performing band-pass filtering and envelope demodulation on each LAIT signal segment separated in the step S1, specifically, performing band-pass filtering on each separated LAIT signal segment to obtain a filtered LAIT signal segment, which is recorded as M'_i,kThen using Hilbert transform to M'_i,kEnvelope demodulation to obtain envelope signal E_i.k；

S3, aligning the LAIT signal segment in step S2 with the phase through autocorrelation, specifically including:

s301, representing the damage impact component in the LAIT signal segment as

Wherein

For the initial phase of the impact, t is time, the autocorrelation function of the damage impact is expressed as:

in the formula (9), tau is time delay, A represents fault impact amplitude of LAIT signal segment, and omega represents fault period T_BThe corresponding angular velocity, then equation (9) is expressed as:

in the formula (10), θ represents a phase,

s302, obtaining the LAIT signal segment envelope signal E according to the autocorrelation function in the step S301_i.kIs expressed as:

in the formula (11), r_i,kBeing a component of an autocorrelation function, L₂Rounding the length of the LAIT signal segment;

s4, performing ensemble averaging on the LAIT signal segments after phase alignment in step S3, performing linear trend item elimination and regularization processing on the ensemble averaged signal to generate an enhanced characteristic signal LAIT-AEA, and then determining whether the bearing has a rolling element fault according to the enhanced characteristic signal LAIT-AEA, specifically including:

s401, the LAIT signal segment of the phase aligned through autocorrelation in the step S3 is subjected to overall average to obtain the rolling element RE_iIs the ensemble average a of the autocorrelation function_iI.e. said rolling elements RE_iIs expressed as:

in the formula (12), τ_jThe time delay of the LAIT signal segment is shown, and K is the number of the LAIT signal segments;

s402, for each rolling element RE in the step S401_iThe overall average characteristic signal is subjected to linear trend item elimination and regularization processing to obtain an enhanced characteristic signal LAIT-AEA, wherein the rolling body RE_iThe linear trend term rejection formula of the overall average characteristic signal is as follows:

in the formula (13), the reaction mixture is,

is to A_iOf the rolling elements RE_iThe regularization processing formula of the ensemble averaged feature signal is as follows:

in the formula (14), min represents taking the minimum value;

and S403, judging whether the bearing has rolling element faults or not through the enhanced characteristic signal LAIT-AEA.

2. The method for diagnosing a bearing fault based on fault-impact extraction and autocorrelation ensemble averaging as claimed in claim 1, wherein the length of the LAIT signal extracted and separated in the step S1 is three rotation cycles of the rolling elements.

3. The method for diagnosing bearing faults based on fault impact extraction and autocorrelation ensemble averaging as claimed in claim 2, wherein the method for extracting and separating the corresponding LAIT signal segment when the rolling element passes through the bearing center in step S1 is implemented as follows:

s101, setting the frequency f of the retainer for the rolling bodies to revolve around the center of the rotating shaft along with the retainer_cThe frequency of the rolling bodies rotating around the centers of the rolling bodies is f_BSThe angle theta of the rolling body rotating around the center of the rotating shaft in one rotation period can be obtained_sComprises the following steps:

θ_s＝2πf_c·T_BS (1)

in the formula (1), T_BS＝1/f_BSThe self-rotation period of the rolling body is T, the corresponding fault period of the rolling body is T_B＝T_BSA fault frequency of f_B＝1/T_B；

S102, setting a rotation period T_BSThe first rolling element passing through the bearing center is designated by the number one rolling element, denoted by RE₁The rolling elements which subsequently pass through the bearing centre are respectively defined as RE₂,RE₃,···,RE_ZWherein Z is the number of rolling bodies, rolling body RE₁Initial phase of

Must satisfy the condition

Then the rolling body RE_iCumulative phase corresponding to jth rotation period

Comprises the following steps:

in the formula (2), the reaction mixture is,

for said rolling body RE₁The phase of the jth autorotation period, delta-2 pi/Z is the central angle between two continuous rolling bodies;

s103, based on rolling element RE_iIt can be seen that the phase of the LAIT signal segment must satisfy the condition:

in the formula (3), the reaction mixture is,

to represent

The remainder of division by 2 pi is represented by formula (2) and formula (n)3) The rolling element RE can be obtained_iThe LAIT signal segment of (1);

s104, according to the accumulated phase sequence in the step S102

Obtaining and accumulating the phase sequence

Corresponding time series t_i,jComprises the following steps:

the time condition for the LAIT signal segment separation is:

T_R-T_BS＜mod(t_i,j+T_BS,T_R)≤T_R (5)

in the formula (5), T_R＝1/f_cIs the rotation period of the holder;

s105, setting the rolling element RE_iIs [ nu ] of the vibration signal₁,ν₂,···,ν_N]Length N, sampling frequency f_sThen the rolling body RE_iMay form a sequence T_iComprises the following steps:

in the formula (6), the reaction mixture is,

is a real number, t_i,1＝t₁-(i-1)δ/(2πf_c)，

Is RE₁Is detected by the phase angle of the phase-locked loop,

the number of the rotation periods is the same as the number of the rotation periods,

represents to Nf_BS/f_sRounding down, then the time sequence satisfying the formula (5) can be found out by the formula (6), and the index corresponding to the time sequence is the index D of the LAIT signal segment_iExpressed as:

in the formula (7), the reaction mixture is,

is a natural number, d_i,kIs RE_iThe index of the kth LAIT signal segment,

the number of LAIT signal segments, the separated rolling elements RE_iIs represented by:

M_i,k＝[ν(d_i,k),ν(d_i,k+1),ν(d_i,k+2),···.ν(d_i,k+(L₂-1))] (8)

in the formula (8), L₂＝[3T_BSf_s]The rounded length of the LAIT signal segment.

4. The method as claimed in claim 3, wherein the band-pass filtering is a resonance band centered on the natural frequency and having several fault frequency sidebands on both sides or a band with a large amplitude energy concentration.

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